What is (\partial)/(\partial x)(xe^{2x}) ?

The answer to (\partial)/(\partial x)(xe^{2x}) is e^{2x}+2e^{2x}x

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(\partial)/(\partial x)(xe^{2x})

\frac{\partial}{\partial x} (x e^{2 x})

e^{2 x} + 2 e^{2 x} x

Solution steps

\frac{\partial}{\partial x} (x e^{2 x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{2 x}

= \frac{\partial}{\partial x} (x) e^{2 x} + \frac{\partial}{\partial x} (e^{2 x}) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{2 x}) = e^{2 x} \cdot 2

= 1 \cdot e^{2 x} + e^{2 x} \cdot 2 x

Simplify

= e^{2 x} + 2 e^{2 x} x

\frac{d y}{d x} = x (y^{2} + 1)

\frac{d y}{d x} = sin (x - y + 7)

\int \frac{3 x + 5}{x ^{2} + 2 x + 1} d x

\frac{\partial}{\partial x} (4 x^{3} y^{3} - 3)

y = \frac{e ^{- x}}{x + 1}, at x = 1

What is (\partial)/(\partial x)(xe^{2x}) ?
The answer to (\partial)/(\partial x)(xe^{2x}) is e^{2x}+2e^{2x}x